In various fields of technology objects are handled which, though of the same type, may vary in their shape. In such a case, it is often necessary to obtain more precise information on this shape for each individual object, as the mere knowledge of the type of object is not sufficient. Such objects may for example be components of an apparatus or device, for instance an electronic device. Due to, usually unavoidable, inaccuracies in manufacturing the components, each component will exhibit deviations from an ideal or nominal shape. A further cause of such deviations is deformations of a specific component which result from mounting the component on further components, for example due to mechanical stresses. The deviations may lead to problems in assembling the respective apparatus or device, which may lead to partial or complete malfunction of the final product.
For example, when manufacturing and/or assembling electronic components (IC packages, substrates, etc.) the actual topography or warpage (deformation) shapes of these components are important in order to ensure proper mechanical and electrical contact with the supporting devices on which these components are mounted. One use-case for which this feature has become even more important is for stacked assemblies where (increasingly smaller) electronic components are stacked on one another. In order to ensure the stacked components used for such assembly are still in proper electrical contact, a classification of the warpage shape of the individual components prior to assembly is required. In this way, components can be sorted into categories which are known to stack well prior to assembly. Another use-case encompasses the categorization of the warpage shape of top and bottom components of stacked devices after assembly to determine matching top and bottom categories.
A known method of categorization is to perform a global second order fit to a surface of interest of the object, and to categorize the object based on the coefficients of this fit. The categories of objects possible by this approach are rather limited, and furthermore are fixed by the geometry of second order surfaces.